The semidirect atom calculus and the ω_χ-decomposition

First stage of the (135)-keystone build (docs/orchestration/p16d6c-keystone-design.md — the authoritative design record; this file implements §§1–2). Contents:

• the raw semidirect calculus on V × C₀ (pmul, pone, associativity — no bundled V ⋊ C group), the transported product maps jmap (into Q = Bg/T) and J (into Bg) with their multiplicativity, and the graph relations tying them to c1a/c1b's fLift/tDef/qOfCocycle;
• the three T-valued defect atoms mDef/conjDef/uDef (the last is Lemma 8.7's class e), and the product formula JDef = conjDef · uDef · mDef;
• the explicit ω_χ-decomposition: χ ∘ JDef = kappa0 (datχ χ) + inflScalar (eχ χ) with datχ χ an equivariant factor-set datum for the zero form — the (130)-normal form of the χ-pushout cover with no abstract extraction.

All std-3, source-generic.

This file is now a thin umbrella: the content lives in the GQ2/KeystoneDelta/ sub-modules imported above (AtomCalculus, ThetaExtraction, AffineAssembly, Keystone).

Paper-tag ledger (auto-generated by paperforge; do not edit)

• Lemma 6.1 = ⟦lem-extraspecialconnecting⟧
• Lemma 8.7 = ⟦lem-affinelifting⟧
• Prop 8.8 = ⟦prop-phaseidentity⟧